Posts Tagged ‘mathematics’

I haven’t posted here for a long time for lots of reasons. For some of those reasons, I think I will now use this blog mostly to write about my craft projects. Posts will probably be quite sporadic, and I make no guarantees!

I have just finished my first project for 2017. I started crocheting a Lorenz Manifold in September 2016, after hearing Dr Hinke Osinga talk about it at the MathsCraft Festival in Auckland. I worked at it fairly steadily for quite a while, then needed to take a break to finish a blanket I wanted to give as a Christmas gift. But I picked it up again, and over the long Wellington Anniversary Weekend I’ve made a push to get the last three rounds (3,200 stitches) completed.

Lorenz Manifold, unmounted

I’m not 100% certain that I’ve marked out the wire guides correctly (you can see them as yellow lines), so I need to check those before I go any further. I’ve sewn in and trimmed all the ends, so it’s ready to go. I’ll post photos of the wired-up final final final product when it’s done!

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Fainjin has the start-of-year blues. “School’s so boring!” he complained. “Everything’s boring!”

“What exactly is boring about it?” I asked.

“Everything!”

“It can’t all be boring. Is lunchtime boring? Playtime?”

“No…” he admitted reluctantly. “Maths is boring. It’s not even proper maths!”

Ah. This takes me back. When I was at primary school, it was the fashion to teach everything in terms of set theory (at least, that’s how I remember it). At the start of every year we would go over the definition of a set, the members of a set, the empty set, union, intersection, cardinality and so on. It was interesting the first time. Every first day of school after that I would stomp into the house and my mother would ask, “How was school?” and I would snarl back, “We did sets. AGAIN.”

“What’s proper maths, then?”

“Like, plus and equals and stuff! Take aways!” the poor boy was pining for sums.

“And what are you doing instead?”

“I don’t even know.” So I took a look at his maths book and discovered they’re doing statistics. How many siblings each classmate has, people’s favourite animals, favourite sports and so on – things that can be counted and expressed in bar graphs. It is maths, and it’s also really good for the kids (and teacher) to get to know each other, since they’ve come from several different Year 2 classes last year.

I had a word to the teacher and he promised to help Fainjin find something “proper” to do too. Meanwhile, I’ve been bribing him to school with the promise of extra addition and subtraction worksheets to do at home or at lunchtime.

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Our school celebrates both academic and sporting success. Children who do well at athletics and swimming get to represent the school at regional and national competitions; children who do well at maths and English are invited to participate in national and international competitions.

Pearl took part in three of these: two for mathematics and one for reading comprehension. She did us proud in all three. Of course, we were proud just to have her selected to participate!

Yesterday Pearl and the other scholars were presented with their certificates at a senior-school assembly. I was struck by the genuinely joyous celebrations of their peers. Some children got certificates for “participation” or “merit” and were soundly applauded. But those who received “distinction” or even “high distinction” were clapped and cheered and the crowd went wild. The pleased blushes of the kids standing up the front were matched by the proud grins of their parents sitting at the back.

I hope these kids will continue to celebrate and recognise academic and scientific success. They’re being trained well.

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It’s the first day of the spring school holidays. Pearl is out with a friend, and Fainjin and Babess and I have just been shopping, now sitting down for some morning tea. There’s some conversation about what we will do with the rest of the day, who needs a drink of water, and so on. Trivialities.

All of a sudden, Fainjin says, “Mum, what numbers can’t you equal?”

I frown at him. “What do you mean?”

“What numbers can’t you equal?”

Does he mean unattainable ages? Imaginary numbers? – unlikely, I don’t think those come up until university-level maths these days and he hasn’t even done multiplication really yet…

“Sweetie, I don’t understand your question. Can you give me an example of what you mean?”

He thinks for a bit. His expression clears… “Well, in colours, you can’t make red or yellow or blue… so what numbers can’t you equal?”

I’m impressed with his analogy. Primary colours are an interesting comparison to prime numbers. As I said, he hasn’t really done multiplication yet – some doubles and halves, counting in twos and fives and tens – but he seems to instinctively grasp the idea that there must be fundamental building blocks in mathematics as well as in art and light.

Explaining prime numbers to a six-year-old without a clear grasp of multiplication is an interesting and delightful experience. Especially when an intrigued five-year-old starts chiming in with more questions.

I can tell these holidays are going to be fun. I really hope he doesn’t start asking about imaginary numbers tomorrow though – I still struggle with those!

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“Oh Mum,” Fainjin assumed his I’m-about-to-tell-you-something-important demeanour, “did you know, one is the most important number?”

Now, I’ve been talking a bit about the “most important” number recently, discussing the nature and history of zero with Pearl and some of the kids at school. So I was interested to hear what Fainjin might have picked up from that, and why he was begging to differ.

“Is it really?”, I enquired. “Why do you think one is the most important number?”

“Oh, because,” he began, “after you get to the last number, you come back around all the way to one again…”

Here we go, another discussion on the nature of infinity with the 5-year-old…!

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While I prepared dinner this afternoon, Fainjin was in the loungeroom colouring in, practising his writing, and – as it turned out – playing about with numbers.

“Hey Mum!” he yelled at me as if there were miles between us instead of just a hallway. “I worked something out! Five plus one, equals, SIX!”

“Yes it does,” I replied, wondering what he might be counting.

A minute later he yelled again. “And five plus two, equals, SEVEN!”

“That’s right.”

Having established a pattern, the next sum was immediate: “Five plus three is EIGHT!”

I put the veges in the oven and went to see what he was up to. He was just writing numbers and adding them up, as far as I could see – not counting anything in particular. “The first one has to be five,” he told me, but I still don’t know quite why. “Five plus five is ten!”

I went back to the kitchen. After a little while, he called out, “Mum! What’s ten plus ten?”

“I think you can figure that out,” I encouraged him.

Later, over dinner, I realised I hadn’t heard his answer. “Did you figure it out?”

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Pearl came home with her homework notebooks and a letter from the teacher today. Last year’s teacher was anti-homework, which suited me just fine. This teacher is following the “school policy” line of 30 min homework per day.

20 minutes of that is supposed to be reading, and I have no problem with that time or proportion. Of course, keeping Pearl down to 20 minutes a day would be an impossible task, and not one I would ever attempt. The suggestions for parents made me raise an eyebrow though. I should read with her, discuss the pictures (pictures?!), ask her what she already knows, what she learns from the text and what might happen next. Help her to sound out words and discuss possible meanings of words she doesn’t recognise. Have her read out simple recipes while I cook them.

That’s all good advice for parents of children learning to read. But Pearl is not learning to read. She is reading to learn, or more often, for enjoyment. She can use a dictionary and has a very wide vocabulary. I know she is ahead of most kids her age (according to standardised testing), but surely most 9 and 10yos in her class aren’t still reading picture books with their parents each night? And I think encouraging her to cook simple recipes herself would be better – that’s reading and maths and life skills all in one.

That brings us to maths. Allthe maths homework is web-based. There are great resources on the web, but I think tailored and directed exercises would be useful too. We try to limit Pearl’s screen/internet time, too, and this is working against that. Plus they want $100 (I am told, haven’t seen a letter from school yet) to subscribe to one of these websites.

Pearl claims not to have been given any spelling homework, despite it being on the “must do” list provided by the teacher. We’ll have to investigate that. Given that one letter home used lots of American spellings and was dated in “Feburary”, I look forward to the spelling homework with some trepidation.

Grumble grumble grumble! And really, all for 10 minutes of work per day, since 20 min of reading is not an issue. But I feel strongly that if you’re going to do homework, it should be of maximum value, not just to fill in the time.

I am lucky, Pearl seems willing to do the homework, at least – probably because it’s mostly reading and playing on the internet. She has to keep a reading log too. All previous attempts at this have ended – with teacher permission – after a week or two, when she has filled several pages and I have noted that we are several books behind because she reads so much and so fast. We’ll see how long this one lasts. If the aim of it is to show the teacher that Pearl reads books, I suspect we won’t have to do it for long.

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About a year ago, a lovely friend came to visit from overseas. Before she left, she gave me a bag of mosaic and craft kits for the children, to be given to them at an opportune time.

I thanked her, and tucked them away “for a rainy day”. And there they stayed.

Yesterday was very rainy. The children played with toys in the morning, and we ventured out in the wet to the local cinema in the afternoon.

Today was, if anything, even more rainy. Cabin fever was setting in. I cleared the kitchen table and called the children to sit down. They were pleasingly mystified, then delighted when they saw what I had for them.

Fainjin’s set was five mosaics – a rocket, a plane, a boat, a helicopter, and a train. He had foam shapes to stick all over them.

Pearl had a “decorate-your-own” tote bag kit, with felt stickers to make her own design.

Babess had a sparkly bunny mosaic. Hers was a paint-by-numbers type (or stick-by-numbers, I suppose), so she needed quite a bit of help with it. Pearl was more than happy to help her.

They all settled down for about two hours, sticking and chatting. Fainjin particularly liked naming the colours and shapes, and pointing out the patterns in his pictures. I told him that “patterns are maths”.

“Hey Daddy!” he crowed, “We’re doing maths!”

He finished two before lunch, then later in the afternoon came asking for the mosaics again. “Mummy, please can I do some more maths?”